Problem: Simplify the following expression: $t = \dfrac{-5n^2 - 40n - 75}{n + 3} $
Answer: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-5$ , so we can rewrite the expression: $ t =\dfrac{-5(n^2 + 8n + 15)}{n + 3} $ Then we factor the remaining polynomial: $n^2 + {8}n + {15} $ ${3} + {5} = {8}$ ${3} \times {5} = {15}$ $ (n + {3}) (n + {5}) $ This gives us a factored expression: $\dfrac{-5(n + {3}) (n + {5})}{n + 3}$ We can divide the numerator and denominator by $(n - 3)$ on condition that $n \neq -3$ Therefore $t = -5(n + 5); n \neq -3$